Spatially resolved monitoring of cable perturbations using multichannel information

ABSTRACT

A monitoring system. The monitoring system may include an optical receiver configured to receive an optical signal, the receiver comprising a plurality of equalizers to partition the optical signal over a plurality of optical channels corresponding to a plurality of optical wavelengths. The monitoring system may also include an analysis component, coupled to the receiver, comprising logic, where the logic is configured to construct a plurality of sensor matrices, corresponding to the plurality of optical channels, based upon the optical signal, after reception at the receiver; determine, using the plurality of sensor matrices, a correlation between at least one pair of sensor matrices corresponding to at least one pair of optical channels of the plurality of optical channels; and determine a location of a perturbation, external to the transmission system, based upon the correlation.

FIELD OF THE DISCLOSURE

This disclosure relates generally to the field of submarinecommunication and relates more particularly to techniques for measuringperturbations using line monitoring equipment.

BACKGROUND

Fiber optic cables connect far-flung continents along the ocean floor,and much of the internee's international traffic travels over thesecables. Generally, communications over fiber optic cables takes placeusing pulses of light that may encounter distortions during transmissionover thousands of kilometers across an ocean. It has been proposed thatperturbations external to an optical fiber, such as earthquakes may bedetected by monitoring changes in optical signals, such as state ofpolarization (SOP) within the fiber. Recently, a change in SOP in anoptical subsea cable has been reportedly detected is response to anearthquake that was located more than one thousand kilometers distantfrom the cable. However, systems and techniques that may detectperturbations whose location is precisely spatially resolved arelacking.

With respect to these and other considerations the present disclosure isprovided.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended asan aid in determining the scope of the claimed subject matter.

A monitoring system may include an optical receiver configured toreceive an optical signal, the receiver comprising a plurality ofequalizers to partition the optical signal over a plurality of opticalchannels corresponding to a plurality of optical wavelengths. Themonitoring system may include an analysis component, coupled to thereceiver, comprising logic, where the logic is configured to construct aplurality of sensor matrices, corresponding to the plurality of opticalchannels, based upon the optical signal, after reception at thereceiver; determine, using the plurality of sensor matrices, acorrelation between at least one pair of sensor matrices correspondingto at least one pair of optical channels of the plurality of opticalchannels; and determine a location of a perturbation, external to thetransmission system, based upon the correlation.

A monitoring system may include a transmitter to generate an opticalsignal, an optical transmission system, comprising an optical cable, totransmit the optical signal, as well as a receiver, to receive theoptical signal. The receiver may include a plurality of equalizers topartition the optical signal over a plurality of optical channels,corresponding to a plurality of optical wavelengths. The monitoringsystem may also include an analysis component, coupled to the receiver.The monitoring system may include logic to: construct a plurality ofsensor matrices, corresponding to the plurality of optical channels,based upon the optical signal, after reception at the receiver. Thelogic may determine, using the plurality of sensor matrices, acorrelation between at least one pair of sensor matrices correspondingto at least one pair of optical channels of the plurality of opticalchannels; and determine a location of a perturbation, external to thetransmission system, based upon the correlation.

A method for monitoring a perturbation may include generating an opticalsignal; conducting the optical signal over a transmission system,comprising an optical cable, over a plurality of optical channels, wherethe plurality of channels correspond to a plurality of wavelengths. Themethod may include detecting the optical signal, after passing throughthe transmission system, at an equalizer of a coherent receiver, andgenerating an equalizer matrix based upon the optical signal for eachoptical channel of at least some optical channels of the plurality ofoptical channels. The method may also include constructing a pluralityof sensor matrices, corresponding to the plurality of optical channels,based upon the equalizer matrix, and extracting a plurality oftime-dependent matrices from the plurality of sensor matrices,respectively. The method may also include generating a normalized sensorcoefficient function from the plurality of time-dependent matrices, thenormalized sensor coefficient function having wavelength as an argument.The method may further include determining a location of a perturbation,external to the transmission system, based upon a characteristic of thenormalized sensor coefficient function.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating an exemplary embodiment of amonitoring system for locating a perturbation, in accordance with thepresent disclosure;

FIG. 1A illustrates an exemplary coherent receiver, consistent withembodiments of the disclosure;

FIG. 1B illustrates an exemplary butterfly architecture for a receiver,consistent with embodiments of the disclosure;

FIG. 2 depicts the general components for creating a sensor matrix,according to embodiments of the disclosure;

FIGS. 3A-3C illustrate normalized sensor coefficient behavior as afunction of wavelength of a probe beam, for three different scenarioscorresponding to different perturbance locations;

FIG. 4A illustrates three different random sensor coefficient behavioras a function of wavelength;

FIG. 4B illustrates an exemplary averaging sensor coefficient functionbased upon the exemplary functions of FIG. 4A;

FIG. 5 illustrates an exemplary sensor coefficient function fordetecting multiple perturbations at different locations; and

FIG. 6 presents an exemplary process flow.

DETAILED DESCRIPTION

The present embodiments may be useful to facilitate detection orperturbances (or perturbations) external to a transmission system, suchas a subsea optical cable. According to embodiments of the disclosure,discussed below, the location of a perturbation may be performed using amonitoring system, equipped with a transmitter system, a coherentreceiver, and a submarine system that includes an optical cable to carrysignals between the transmitter and receiver along multiple opticalchannels. Generally, a monitoring system of the present embodiments maybe integrated into a bidirectional optical communication system. Invarious embodiments, it will be understood that a transmitter system mayrepresent a plurality of transmitters and a receiver may represent aplurality of receivers, in a bidirectional optical communication system.Moreover, each transmitter may be coupled for bidirectionalcommunication with a dedicated receiver as a transmitter-receiver pairthat links the transmitter and receiver through a dedicatedcommunication channel. The monitoring system may further include ananalysis component to generate and analyze a plurality of sensormatrices that are constructed from a corresponding plurality of opticalchannels (also referred to herein merely as “channels”) in the opticalcable. The present embodiments exploit the differences in signalsreceived among different channels in a multichannel optical cable. Byexamining the correlation between different sensor matrices constructedfrom signals received through the different channels, the proximity of aperturbation may be determined.

According to various embodiments of the disclosure, the correlation ofsensor matrices is performed by taking into account several factors: 1)The further away (in frequency or wavelength) a given set of opticalchannels are from one another, the less corelated their sensor matricesbecome; 2) the closer to the receiver end the perturbation is, thelarger are the correlations between given sensor matrices; 3)correlations depend on fiber PMD (polarization mode dispersion), whichparameter is a known parameter for a given optical fiber. Theaccumulated fiber PMD is an entity that destroys the correlations, thusencoding information about the distance from a perturbation point. Saiddifferently, the longer the propagation distance between a receiver anda perturbation point, the more PMD is accumulated, the more thecorrelation is destroyed.

FIG. 1 is a schematic diagram illustrating an exemplary embodiment of amonitoring system 100 for detecting and locating a perturbation 120, inaccordance with the present disclosure. The monitoring system 100includes a transmitter system 102, such as an assembly of transmitters,each having a laser source, to generate an optical signal, which signalmay be a plurality of simultaneously-launched signals, deemed to be aprobe beam 110. The probe beam 110 maybe broadened to a targetedbandwidth, in the range of 25 MHz, such as 10 MHz, 25 MHz, 50 MHz, 100MHz, or similar value according to various non-limiting embodiments. Invarious embodiments, where the transmitter system 102 represent aplurality of transmitters, and where each transmitter may have aseparate laser source, a given laser source may be coupled to a givencommunication channel. Accordingly, the probe beam 110 may representmultiple signals that are launched from a plurality of laser sources ina respective plurality of transmitters. Likewise, the multiple signalsmay be transmitted simultaneously over a plurality of communicationchannels, in particular, at least two communication channels. Accordingto embodiments of the disclosure, exemplary wavelengths for thecommunication channels may span the known C-band or L-band, near 1550 nmwavelength.

The probe beam 110 may be transmitted through a submarine system 104,including an optical cable (not separately shown), configured totransmit the probe beam 110 over multiple channels, where the multiplechannels correspond to the different channels of the transmitter system102 corresponding to different wavelengths of the probe beam 110. Thus,the multiple channels may be carried over optical fibers of the opticalcable. Note that in various embodiments, the submarine system 104 mayinclude an optical cable whose fibers serve both as multiplecommunication channels for bidirectional communication of (payload)information, as well as to conduct the probe beam 110 over the samemultiple communication channels.

The monitoring system 100 may further include a receiver 106, such as acoherent receiver, as described below. As detailed below, the receiver106 may represent a plurality of equalizers that operate to receive theprobe beam over a series of channels, corresponding to differentwavelengths. In particular, the receiver 106 may be coupled to receiveinformation over the multiple channels of the monitoring system 100,such as normal information-carrying channels that are used to alsoconduct the probe beam 110.

The monitoring system 100 may further comprise an analysis component108, coupled to the receiver 106, to generate and analyze a plurality ofsensor matrices that are constructed from a corresponding plurality ofchannels in the submarine system 104. The analysis component 108 mayinclude a combination of hardware and software, including logic toperform the operations as detailed in the embodiments to follow. Notethat the analysis component 108 may communicate with the receiver 106 toextract information received by the receiver 106. For example, theanalysis component may be embodied in any combination of computer,processor, software, and may be located at any convenient location ofthe monitoring system 100, and not necessarily proximate to thetransmitter system 102, receiver 106, or submarine system 104.

FIG. 1A illustrates the general architecture of a receiver 106,consistent with embodiments of the disclosure. FIG. 1B illustrates anexemplary butterfly architecture for a receiver 106, consistent withembodiments of the disclosure. The receiver 106 may be configured as inknown coherent receivers, with an equalizer having a butterfly structure(EQ) as part of the coherent receiver DSP, as generally illustrated inFIG. 1B.

As shown, an input signal is received, and a local oscillator (LO) isprovided to interfere with the input signal, where the LO may have thesame frequency as the transmitter laser in the 90-degree optical hybriddevice. The input signal may represent the probe beam 110 of FIG. 1 . Inorder to detect both in phase and quadrature components, the inputsignal may be mixed along one path with the in-phase part of the LO andmixed with the quadrature component in another path through the90-degree phase delay between the signal and the LO introduced by the90-degree hybrid. The electrical signal may be digitalized usinganalog-to-digital converters (ADC)s.

Thus, save for the addition of the analysis component 108, the generalarchitecture and hardware of the monitoring system 100 may be embodiedin known components of a known subsea bidirectional communicationsystem, including a plurality of transmitter/receiver pairs that eachcommunicate over a dedicated optical channel.

In various embodiments, the analysis component 108 may extractinformation transmitted via the probe beam 110 across the submarinesystem 104 and received by the receiver 106, in order to determine thelocation of a perturbation that modifies the probe beam 110 in a mannerso as to affect the correlation of signals transmitted across thedifferent channels of the submarine system 104. Said differently, thepresent embodiments may determine the location of a perturbationaccording to the manner in which the perturbation affects thedecorrelation of signals across the different wavelengths correspondingto the different channels of the probe beam.

Following the general example of FIG. 1B, a coefficient h, derived fromthe input signal, may be used to form an equalizer matrix H, whichmatrix can be thought of as a compensation for system-induced signaldistortions. Often, each element of the equalizer matrix H has multipletaps (each tap associated with a different time delay). Thisconfiguration is equivalent of having an optical channel band split intosub-bands, with each sub-band having its own “single tap” butterflystructure equalizer. Consequently, the values of equalizer matrix H foreach sub-band can be extracted from the values of multi-tap equalizercoefficients. Thus, each sub-band has its own matrix H, and eachsub-band can be treated as a channel.

According to embodiments of the disclosure, the equalizer matrix H maybe used to construct a sensor matrix, as described in the following. Foreach channel, as illustrated in FIG. 2 , a system Jones matrix M(λ, t)is reconstructed as inverse of the equalizer matrix H⁻¹(λ, t). Let'sdefine Average (over time) inverse matrix A: Â(λ)≡<{circumflex over(M)}(λ, t)>⁻¹. In accordance with embodiments of the disclosure, oncethe matrices M⁻¹ (or equivalently, H) are known for each channel of asubmarine system, the construction of a sensor matrix S may follow. Thesenor matrix S is generally constructed as a multiplication ofestimation of the matrix M (which is an estimation of the transmissionsystem (subsea optical system) with time dependent perturbations) andthe Inverse unperturbed system matrix A. Said differently, the sensormatrix S may be calculated as: Sensor Matrix=Ŝ(λ, t)={circumflex over(M)}(λ, t)·Â(λ), where the “·” symbol represents a matrixmultiplication.

Note that for a given transmission system of a subsea system, eachchannel has its own sensor matrix S. In this approach, an assumption isthat removal of perturbations from the transmission matrix can beachieved by time averaging over time. Such a construction removesdifferences between channels that may accumulate before the differentchannels are combined into a single fiber, as well as differencesoccurring after the different channels split into different paths beforedetection (with the assumption that the channels are not perturbed overtime before combining and/or after splitting). The sensor matrix S, thusconstructed, is a function of both time and wavelength (oralternatively, channel index).

In accordance with various embodiments of the disclosure an entity thatis used to determine the location of a perturbation is constructed fromthe sensor matrix S. This entity is termed a normalized sensorcoefficient, which coefficient may be constructed as follows:

A time-varying component of the sensor matrix S is extracted as thematrix {circumflex over (R)}(t), as detailed below with respect to Eq.(7). Let r_(i,j)(λ, t) be elements of matrix {circumflex over (R)}(t).Let s_(i,j)(λ, f) be the Fourier transform of r_(i,j)(λ, t). Theperturbation amplitude is proportional to s, and can be extracted atthis point. In accordance with some embodiments, this entity can beaveraged over wavelength.

For purposes of simplification, an in accordance with some embodimentsof the disclosure, a perturbation may be monitored at a given frequencyof interest f (e.g., earthquake frequency), and accordingly f will thusbe omitted in the formulae to follow. For a given indexes i and j anormalized sensor Coefficient C is introduced, as follows:

$\begin{matrix}{{C\left( {\lambda_{1},\lambda_{2}} \right)} \equiv {{{Re}\left\lbrack \frac{{s\left( \lambda_{1} \right)}{s^{*}\left( \lambda_{2} \right)}}{\sqrt{{❘{s\left( \lambda_{1} \right)}❘}{❘{s\left( \lambda_{2} \right)}❘}}} \right\rbrack}.}} & (1)\end{matrix}$

In this example, the sensor coefficient C is a function of twowavelengths (or channel indexes). As noted, this normalized sensorcoefficient is for a particular perturbation frequency of interest.Alternatively, each perturbation frequency can be characterized by adifferent sensor coefficient C.

According to embodiments of the disclosure, by monitoring the sensormatrices, perturbations that may affect the transmission system can bedetected and located. Because the sensor matrix is a function ofwavelength, the behavior of sensor matrix as a function of wavelengthmay provide an indication of the nature and location of a perturbation.In the absence of a perturbation, the following conditions will apply:

{circumflex over (M)}(λ, t)=<{circumflex over (M)}>≡

(λ)   (2A)

Ŝ(λ, t)=I   (2B)

For a small periodic perturbation {circumflex over (P)}(t) at thereceiver end of system (where P(t) is the same for any channel), thefollowing conditions will apply:

{circumflex over (M)} ^(pert)(t)=(I+{circumflex over (P)}(t)·

(λ)   (3)

(λ)≈<{circumflex over (M)}(λ, t)>  (4)

Ŝ(t)=(I+{circumflex over (P)}(t))   (5)

In this scenario, as shown in Eq. (5). the sensor matrix behavior doesnot register any wavelength dependence.

For a perturbation {circumflex over (P)}(t) at system beginning, thefollowing conditions apply:

$\begin{matrix}{{{\hat{M}}^{pert}(t)} = {(\lambda) \cdot \left( {I + {\hat{P}(t)}} \right)}} & (6)\end{matrix}$ $\begin{matrix}{{\hat{S}\left( {\lambda,t} \right)} = {{{(\lambda) \cdot \left( {I + {\hat{P}(t)}} \right) \cdot}(\lambda)^{- 1}} = {{I + {{(\lambda) \cdot {\hat{P}(t)} \cdot}(\lambda)^{- 1}}} = {I + {\hat{R}\left( {\lambda,t} \right)}}}}} & (7)\end{matrix}$

Note that in Eq. 7, the matrix {circumflex over (R)} represents thetime-dependent part of the sensor matrix S. In the above manner, thewavelength (or channel index) behavior in the sensor matrix encodeswhere a perturbation is located.

FIGS. 3A-3C illustrate normalized sensor coefficient behavior as afunction of wavelength of a channel of a probe beam, for three differentscenarios corresponding to different perturbance locations.

In particular, the three graphs shown in FIGS. 3A-3C show behavior ofthe normalized sensor coefficient C as a function of one of itsarguments for three different locations of a perturbation with respectto the transmission system (equivalent to an optical cable). Generally,the variation in sensor coefficient with wavelength is very differentamong the different cases. The functions shown in FIGS. 3A-3Cessentially show the correlation of sensor matrices for differentchannels, expressed as a function of wavelength. In the case of theperturbation being located at the transmission system end (FIG. 3A),there is no wavelength dependence for sensor coefficient. For FIGS. 3Band 3C, the vertical dashed line shows a characteristic of thenormalized sensor coefficient function, in this case a so-called“deviation from 1 location” where the normalized sensor coefficient Cbecomes essentially less than one, and the delta of wavelengths λ₂−λ₁(or of channel indexes) relates to the location of perturbation andfiber PMD. The determination of the point where the sensor coefficientbecomes essentially less than one may be performed in different manners.One example, is provided in FIG. 4B. In the case of the perturbationbeing located in the middle of the transmission system (FIG. 3B), thereis a gradual decay in C between λ₁ and λ₂, with larger fluctuationstowards λ₂. In the case of the perturbation being located in thebeginning of the transmission system (FIG. 3B), there is a more rapidinitial decay in C between λ₁ and λ₂, again with larger fluctuationstowards λ₂.

Note that for the latter two cases represented by FIG. 3B and FIG. 3C,where normalized sensor coefficient C varies with wavelength, this“deviation from 1 location” is somewhat random when just a single Ccoefficient is considered. In accordance with various embodiments of thedisclosure, the randomness of the normalized sensor coefficient C as afunction of one of its parameters may be significantly reduced byperforming averaging over the other channels. To explain this latterapproach, FIG. 4A illustrates three different random sensor coefficientbehaviors as a function of wavelength, while FIG. 4B illustrates anexemplary averaging sensor coefficient function based upon the exemplaryfunctions of FIG. 4A. As particularly illustrated in FIG. 4A, a sensorcoefficient C(λ₁, λ₂) is shown for three different cases where thechanges in the value of C as a function of wavelength differ markedlybetween each case. In each case, the value of C generally decreases, butthe fluctuations in the value of C are qualitatively different among thedifferent curves.

Turning now to FIG. 4B, there is shown a curve representing an averagingfunction {tilde over (C)}(Δλ) that is a function of delta lambda (ordelta frequency or delta channel indexes). In this function, the valueof {tilde over (C)}(Δλ) is a monotonically decaying function. Thisfunction is better suited to find the “deviation from 1” location, suchas the location where the function value is equal to e⁻¹. This locationin terms of Δλ is related to the physical location of a perturbationalong the transmission system. In particular, the distance L may bedetermined according to the following equations

$\begin{matrix}{\frac{{PMD}^{2}\Omega^{2}L}{3} \approx 1} & (8)\end{matrix}$

where PMD is a system polarization mode dispersion and Ω is the radialfrequency difference between channels,

$\begin{matrix}{{\Omega = {{2{\pi\left( {f_{1} - f_{2}} \right)}} \approx {\frac{2\pi c}{\lambda^{2}}\Delta\lambda}}},} & (9)\end{matrix}$

where c is the speed of light. Note that according to known approaches,the correlation between polarizations in two channels will decorrelateby a value of 1/e in the presence of PMD along the length of the link L,and separation Ω. Thus, the Δλ value where {tilde over (C)}(Δλ)decreases to 1/e is used in equation (8) to determine the value of L.

In one embodiment, for generating the curve of FIG. 4B, the fitting maybe achieved by adjusting just one parameter γ, as explained below.

As shown in the curves of FIG. 4A, we have normalized sensor coefficientfunctions C(λ_(i), λ₂) where i is the channel index (FIG. 4A shows i=1,11, . . . 21) corresponding to different optical channels. As a firstmatter, the functions C can be transformed into functions of Δλ:

C_(i)(Δλ)≡C(λ_(i), λ_(i)+Δλ)   (10)

Secondly, finding an average is performed:

$\begin{matrix}{{C_{ave}\left( {\Delta\lambda} \right)} = {\frac{1}{N}{\sum_{i = 1}^{N}{C_{i}\left( {\Delta\lambda} \right)}}}} & (11)\end{matrix}$

where N is the number of functions C_(i)(Δλ) that we have. Here theassumption is that C_(i)(Δλ) are normalized to 1 when Δλ=0, so theaverage function C_(ave)(Δλ) is automatically normalized to 1 also, thatis, the process of averaging should not change that normalization.Therefore C_(ave)(Δλ) can be best fit by function exp (−γ(Δλ)²) byadjusting just a single parameter γ, since the function exp (−γ(Δλ)²)equals to 1 for Δλ=0. Mathematically, the following integral (which canbe approximated as sum in numerical evaluation) is minimalized byadjusting the value of γ:

∫₀ ^(max)(C _(ave)(Δλ)−exp(−γ(Δλ)²)²))²dΔλ→min   (12)

Once the value of γ is found, the value of Δλ_(PMD) from FIG. 4 .B canbe calculated as:

Δλ_(PMD)=1/γ  (13),

leading to the value of L, or perturbation distance, from substitutingΔλ_(PMD) into Eqs.9, in order to determine Ω.

In other embodiments, a normalized sensor coefficient may be determinedby averaging over both time and over f. In still further embodiments, toconstruct an averaging sensor coefficient function, from which functionthe perturbation location is determined, averaging may take place over 4coefficients of s_(i,j)(λ, f).

While the aforementioned embodiments are generally illustrative of theuse of a sensor matrix to detect a single perturbation, when more thanone location experiences a perturbation along a transmission system, thefunction {tilde over (C)}(Δλ) may have a more complex shape than thoseillustrated so far. According to further embodiments of the disclosure,a sensor coefficient function may be analyzed to generate multipleperturbation locations. To illustrate this approach, FIG. 5 shows anexemplary sensor coefficient function for detecting multipleperturbations at different locations.

Note that the curve shown in FIG. 5 presents a simplification of asensor coefficient function that may arise in the presence of more thanone perturbation. As in FIG. 4 , the sensor coefficient function {tildeover (C)}(Δλ) function may be an averaging function where the valuegenerally decreases as a function of Δλ. In the illustration of FIG. 5 ,the assumption is that two perturbations are present at differentlocations along a transmission system. The sensor coefficient functionof FIG. 5 exhibits two distinct regions of rapid decrease in value. Afirst perturbation location L₁ may be determined from the position ofthe first vertical dashed line, representing Δλ_(PMD) ₁ while a secondperturbation location L₂ may be determined from the position of thesecond vertical dashed line, representing Δλ_(PMD) ₂ . In each case, thegiven Δλ value may represent the point where the sensor coefficientfunction, which function may be an average normalized sensor coefficientfunction, as detailed above, decreases below a respective thresholdvalue. Thus, for the first perturbation location

$\frac{{PMD}^{2}\Omega^{2}L_{1}}{3} \approx 1$

while for the second perturbation location

$\frac{{PMD}^{2}\Omega^{2}L_{2}}{3} \approx 1.$

The amplitude of each perturbation is proportional to “step size” in thesensor coefficient function. In one embodiment, the shape of the sensorcoefficient function may be fitted as combination of two Gaussianfunctions with different sigmas (width) and amplitude coefficients. Thewidth information of each function carries information about thelocation of the perturbation, and the amplitude coefficient carriesinformation about perturbation strength. Thus both perturbation locationand strength can be extracted from the function of FIG. 5 .

FIG. 6 presents an exemplary process flow 600, according to someembodiments of the disclosure. At block 602, a probe beam is launchedfrom a transmitter system, including multiple transmitters. In variousembodiments, the transmitter system may transmit the probe beam from aplurality of transmitters that each include a laser source and each arecoupled to a separate communication channel. As such, the probe beam mayconstitute a conventional set of signals launched over plurality ofwavelengths corresponding to existing information-carrying channels inan existing bi-directional optical communication system.

In some embodiments, the probe beam may be launched over a plurality ofchannels that may be separate from normal information-carrying channels.In particular, an adjustable wavelength signal may be launched over adedicated fiber at a wavelength not corresponding to informationcarrying channels.

At block 604, the probe beam is directed through multiple channels of atransmission system, corresponding to multiple different wavelengths.The multiple channels may extend for hundreds of kilometers along asubsea transmission system, for example. The multiple channels may becombined into a single fiber and may be split into different paths alongthe transmission system. In various embodiments, the number of channelsconducting the probe signal may range between 2 and 300.

At block 606, the probe beam is detected at a sensor over the multiplechannels. The sensor may be arranged as a coherent receiver having anequalizer with a butterfly structure, according to some embodiments.

At block 608, a sensor matrix S is constructed for each channel, basedupon the detected probe beam over the multiple channels. The sensormatrix S may be constructed as multiplication of estimation of matrix M(which is estimation of system with time dependent perturbations) and anInverse unperturbed system matrix A.

For example, an equalizer matrix, represented by M⁻¹ may be constructedfrom a system matrix M(λ, t) that is generated based upon thetransmitted channel Tc for each channel. More particularly, theequalizer matrix is constructed as a Jones matrix Average Inverse (overtime): Â(λ)≡<{circumflex over (M)}(λ, t)>⁻¹. In particular, the sensormatrix S may be calculated as: Sensor Matrix: Ŝ(λ, t)={circumflex over(M)}(λ, t)·Â(λ), where the “·” represents matrix multiplication.

In some variants, the matrix H (M⁻¹) may be extracted when channels aremathematically separated into virtual sub-channels (or sub-bands) on thereceiver side, where the matrix can be calculated separately for eachvirtual subchannel. Note that in these variants, additional software maybe employed in an analysis component to perform the virtual sub-channelcalculations, while not impacting information transmitted through thegiven information-carrying communication channels of a bidirectionaloptical communication system. In this case the step over delta lambda inFIG. 4 will be defined by bandwidth of the virtual subchannels(sub-bands).

At block 610, a time-dependent matrix R is constructed from the sensormatrix S. In one implementation the matrix R is extracted from thesensor matrix S as follows;

Ŝ(λ, t)=

(λ)·(I+{circumflex over (P)}(t))·

(λ)⁻¹ =I+

(λ)·{circumflex over (P)}(t)·

(λ)⁻¹ =I+{circumflex over (R)}(λ, t).

At block 612, a Fourier transform of matrix R is performed to determineSensor Fourier coefficients S_(i,j)(λ, f).

At block 614, a normalized sensor coefficient function is constructed asa function of wavelength from the sensor Fourier coefficients. Thenormalized sensor coefficient function may omit the frequency dependenceof the sensor Fourier coefficients in some embodiments. For example,when monitoring the received power over a plurality of wavelengths inthe presence of a possible perturbance, the perturbance may be monitoredat a given frequency of interest f (e.g., earthquake frequency), so thatthe normalized sensor coefficient is monitored over wavelength atconstant frequency. For indexes i and j the normalized sensorCoefficient may thus be constructed as follows:

${C\left( {\lambda_{1},\lambda_{2}} \right)} \equiv {{{Re}\left\lbrack \frac{{s\left( \lambda_{1} \right)}{s^{*}\left( \lambda_{2} \right)}}{\sqrt{{❘{s\left( \lambda_{1} \right)}❘}{❘{s\left( \lambda_{2} \right)}❘}}} \right\rbrack}.}$

At block 616, the location of perturbation is determined based uponcharacteristic feature of normalized sensor coefficient function. In oneexample, the location of the perturbation may be determined based upon a“deviation from 1 location” where the sensor coefficient C becomesessentially less than one, and the delta of wavelengths λ₂−λ₁ (or ofchannel indexes) relates to the location of perturbation and fiber PMD.

In particular, the distance L, defining the location of theperturbation, may be determined according to the following equation:

$\frac{{PMD}^{2}\Omega^{2}L}{3} \approx 1$

where Ω represents and Ω is the radial frequency difference betweenchannels, Ω=2π(f₁−f₂), and PMD is a system constant.

As used herein, an element or step recited in the singular and proceededwith the word “a” or “an” should be understood as not excluding pluralelements or steps, unless such exclusion is explicitly recited.Furthermore, references to “one embodiment” of the present disclosureare not intended to be interpreted as excluding the existence ofadditional embodiments that also incorporate the recited features.

While the present disclosure makes reference to certain embodiments,numerous modifications, alterations and changes to the describedembodiments are possible without departing from the sphere and scope ofthe present disclosure, as defined in the appended claim(s).Accordingly, it is intended that the present disclosure not be limitedto the described embodiments, but that it has the full scope defined bythe language of the following claims, and equivalents thereof.

1. A monitoring system, comprising: an optical receiver configured toreceive an optical signal, the receiver comprising a plurality ofequalizers to partition the optical signal over a plurality of opticalchannels corresponding to a plurality of optical wavelengths; and ananalysis component, coupled to the receiver, comprising logic, the logicto: construct a plurality of sensor matrices, corresponding to theplurality of optical channels, based upon the optical signal, afterreception at the receiver; determine, using the plurality of sensormatrices, a correlation between at least one pair of sensor matricescorresponding to at least one pair of optical channels of the pluralityof optical channels; and determine a location of a perturbation,external to the transmission system, based upon the correlation.
 2. Themonitoring system of claim 1 further comprising an optical cable coupledto the optical receiver, the optical cable being characterized by afiber polarization mode dispersion (PMD), wherein the correlation isbased at least in part upon the fiber PMD.
 3. The monitoring system ofclaim 2, wherein the optical cable is part of an optical transmissionsystem extending from a first location to a second location, thecorrelation at the first location has a first value, and wherein thecorrelation at a second location has a second value, greater than thefirst value, wherein the second location is closer to the receiver thanthe first location.
 4. The monitoring system of claim 1, wherein eachoptical channel of the plurality of optical channels is represented by agiven sensor matrix of the plurality of sensor matrices, wherein thegiven sensor matrix is represented by: Ŝ(λ, t), the logic to constructthe given sensor matrix from a system matrix {circumflex over (M)}(λ,t), wherein: Ŝ(λ, t)={circumflex over (M)}(λ, t)·Â(λ); whereinÂ(λ)≡<{circumflex over (M)}(λ, t)>⁻¹.
 5. The monitoring system of claim4, the logic to construct the given sensor matrix,: Ŝ(λ, t), from aperiodic perturbation, wherein the periodic perturbation is given by{circumflex over (P)}(t), wherein Ŝ(λ, t)=I+{circumflex over (R)}(λ, t),where I represents the given sensor matrix in an absence of the periodicperturbation, and wherein {circumflex over (R)}(λ, t)=

(λ)·{circumflex over (P)}(t)·

(λ)⁻¹.
 6. The monitoring system of claim 5, wherein the correlationcomprises a normalized sensor coefficient, C(λ₁, λ₂), wherein a value ofthe normalized sensor coefficient varies as a function of difference inwavelength, between a first wavelength λ₁, and a second wavelength, λ₂.7. The monitoring system of claim 6, the logic to determine the locationof the perturbation based upon a value of the difference in wavelengthwhen the value of the normalized sensor coefficient decreases to a levelbelow
 1. 8. The monitoring system of claim 6, wherein the logic todetermine the location of the perturbation by averaging a plurality ofnormalized sensor coefficient functions, as a function of difference inwavelength.
 9. The monitoring system of claim 8, the logic to determinethe location, L, of the perturbation by determining a fiber polarizationmode dispersion (PMD), wherein$\frac{{PMD}^{2}\Omega^{2}L}{3} \approx 1.$
 10. The monitoring system ofclaim 7, the logic to determine a plurality of locations L₁, L₂, of aplurality of perturbations, based upon a plurality of values of thedifference in wavelength when the value of the normalized sensorcoefficient decreases to a plurality of respective threshold values. 11.A method for monitoring a perturbation, comprising: generating anoptical signal; conducting the optical signal over a transmissionsystem, comprising an optical cable, over a plurality of opticalchannels, the plurality of optical channels corresponding to a pluralityof wavelengths; detecting the optical signal, after passing through thetransmission system, at an equalizer of a coherent receiver; generatingan equalizer matrix based upon the optical signal for each opticalchannel of at least some optical channels of the plurality of opticalchannels; constructing a plurality of sensor matrices, corresponding tothe plurality of optical channels, based upon the equalizer matrix;extracting a plurality of time-dependent matrices from the plurality ofsensor matrices, respectively; generating a normalized sensorcoefficient function from the plurality of time-dependent matrices, thenormalized sensor coefficient function having wavelength as an argument;and determining a location of a perturbation, external to thetransmission system, based upon a characteristic of the normalizedsensor coefficient function.
 12. The method of claim 11, the opticalcable being characterized by a fiber polarization mode dispersion (PMD),wherein the characteristic is based at least in part upon the fiber PMD.13. The method of claim 11, wherein, at a first location along theoptical transmission system, the normalized sensor coefficient functionhas a first value, and wherein at a second location along the opticaltransmission system, the normalized sensor coefficient function has asecond value, greater than the first value, wherein the second locationis closer to the receiver than the first location.
 14. The method ofclaim 11, wherein a given sensor matrix, corresponding to a givenoptical channel of the plurality of optical channels is represented by:Ŝ(λ, t), wherein the given sensor matrix is constructed from a systemmatrix {circumflex over (M)}(λ, t), wherein: Ŝ(λ, t)={circumflex over(M)}(λ, t)˜Â(λ); wherein Â(λ)≡<{circumflex over (M)}(λ, t)>⁻¹.
 15. Themethod of claim 14, wherein the given sensor matrix, is constructed froma periodic perturbation, wherein the perturbation is a periodicperturbation, given by {circumflex over (P)}(t), wherein Ŝ(λ,t)=I+{circumflex over (R)}(λ, t), where I represents the given sensormatrix in an absence of the periodic perturbation, and wherein{circumflex over (R)}(λ, t)=

(λ). {circumflex over (P)}(t)·

(λ)⁻¹.
 16. The method of claim 15, wherein the normalized sensorcoefficient function represents a variation is an sensor coefficient Cas a function of difference in wavelength, between a first wavelengthλ₁, and a second wavelength, λ₂.
 17. The method of claim 16, wherein thelocation of the perturbation is determined based upon a value of thedifference in wavelength when a value of the normalized sensorcoefficient function decreases to a threshold value below
 1. 18. Themethod of claim 16, wherein the location of the perturbation isdetermined by averaging a plurality of normalized sensor coefficientfunctions, as a function of difference in wavelength.
 19. The method ofclaim 18, wherein the location, L, of the perturbation is determined bydetermining a fiber polarization mode dispersion (PMD), wherein$\frac{{PMD}^{2}\Omega^{2}L}{3} \approx 1.$
 20. The method of claim 17,wherein a plurality of locations L₁, L₂, of a plurality ofperturbations, is determined based upon a plurality of values of thedifference in wavelength when the value of the normalized sensorcoefficient decreases to a plurality of threshold values below 1.